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Kubo-Greenwood for transport properties from First Principle Molecular Dynamics with VASP

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# *__KG4VASP__*

__version__: v1.0 stable (stand alone)  
Application to real systems: ref. to scientific journal [1] in References

## Acknowledgements:

I would like to thank:

* kgec developers 1 for their inspiring work and effort to deliver a nice tool for *QE*
* for the mathematical derivation of various quantities from the generalised Kubo-Greenwood formula 2
* *Quantum espresso* 3
* *VASP* 4

## The code
This code is meant to be as a VASP post-processing tool for people that want to calculate transport properties.

The quantities calculated at the moment are:

1. Electrical conductivity/resistivity

2. Seebeck coefficient

3. Electron thermal conductivity

4. Possibly, a flavour of the relaxation time $\tau$ can be obtained by fitting $\sigma (\omega) = \sigma_0 / 1+\omega^2 \tau^2$ at $\omega \rightarrow 0$ (Drude Model)

####   The INPUT file
    *kg4vasp* input file is called INPUT and needs that  the following FLAGS have to be addressed:

* SYSTEM (character): usually name of the system in study
    * NBANDS (integer): number of bands
    * FILE_NABLA (character): name of file where the DFT code stores nabla matrix elements
    * NKPOINTS (integer): number of K-POINTS
    * NP_FREQ (integer): number of frequency between min and max
    * DELTAE (real): energy threshold for degeneracy between two contiguous energies
    * MAX_FREQ (real): max value for frequency in eV
    * MIN_FREQ (real): min value for frequency in eV
    * GAUS_SIGMA (real): spreading in eV for delta function that is approximated by 1 gaussian function  
    * VOLUME (real): cell volume in $Ang ^3$
    * DEGAUSS (real): electronic temperature $K_b \cdot  T$ (degauss in quantum espresso and sigma in VASP if the smearing has been set up on ) in eV
    * INTRA_BAND (boolean): **TRUE**=in the calculation intraband and degerate energies are included; **FALSE**=other way round
    * FERMI_ENERGY (real): fermi energy from SCF (STATIC DFT CALCULATION) in eV
    * FROM_VASP (boolean): **TRUE**=post-processing of VASP calculations; **FALSE**=post-processing of QE calculations
    * OCC_FROM_CODE (boolean):
    * N_ELECTRON (integer): total number of electrons in the system
    * NABLA_BIN (boolean, default=**.FALSE.**): **TRUE**: the nabla file is in binary format; **FALSE** the nabla file is in ASCII formatted file.

## The repository
The structure is the following:

1. src: source code in fortran90
    * check Makefile to update the fortran compiler: a) compile with *make* or 2) clean with *make clean*
2. examples: test drive for kg4vasp
    a) Simple VASP calculations
    b) from kgec code simple QE/kgec calculations
    c) comparison between them and validation
3. PATCHES: necessary for kgec v2.1 and VASP 5.4.4 to run kg4vasp on VASP matrix elements and on kgec/QE output as well.

## Reference

1. [C. Di Paola, F. Macheda, S. Laricchia, C. Weber, and N. Bonini. Phys. Rev. Research, 2, 033055 (2020)](https://doi.org/10.1103/PhysRevResearch.2.033055)

2. [L. Calderín, V. V. Karasiev, S. B. Trickey, Computer Physics Communications Volume 221, December 2017, Pages 118-142](https://doi.org/10.1016/j.cpc.2017.08.008)

3. [S. Mazevet, M. Torrent, V. Recoules, F. Jollet, High Energy Density Physics Volume 6, Issue 1, January 2010, Pages 84-88]( https://doi.org/10.1016/j.hedp.2009.06.004)

4. [P. Giannozzi, S. Baroni, *et al* J.Phys.:Condens.Matter 21, 395502 (2009)](http://dx.doi.org/10.1088/0953-8984/21/39/395502)

4. [G. Kresse and J. Hafner, Phys. Rev. B 47 , 558 (1993); ibid. 49 , 14 251 (1994)](https://doi.org/10.1103/PhysRevB.47.558)

kg4vasp

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